## Abstract

In this paper the topic of the safety assessment of masonry arches based upon their geometry is investigated. The theoretical background is the Heymanian master safe theorem along with the no-tension assumption of masonry. The continuous arch is analyzed considering a discrete pattern of vertical loads, such as those of the self-weight and superimposed loads. Among all the lines of thrust contained within the profile of the arch, the one closest to the geometrical axis can be considered to be the best one thanks to the minimum bending moment and shear force present in each cross section. A numerical procedure for computing the line of thrust closest to the geometrical axis of an arch subject to its self-weight has been recently formulated by the authors. This procedure accounts for this line of thrust by minimizing the distances between the geometrical axis of the arch and the thrust line. In order to consider the action of both vertical loads and horizontal forces proportional to the vertical ones, such as those provoked by an earthquake, an extension of this procedure is herein presented. The safety of the arch is finally assessed by computing a domain of equilibrium thrust lines within the profile of the arch which provides, in analogy with the Heymanian geometrical factor of safety, the full range factor of safety. The procedure is described in the paper and illustrated with regards to the analysis of arches subject only to vertical loads and arches subject to also horizontal forces.

## References

[1] Alecci, V. Stipo, G. La Brusco, A., De Stefano, M. and Rovero, L. Estimating elastic modulus of tuff and brick masonry: a comparison between on-site and laboratory tests. Constr. Build. Mater. (2019) 204:828-38.

[2] Block, P., Ciblac, T. and Ochsendorf, J. Real-time limit analysis of vaulted masonry buildings. Comput. Struct. (2006) 84:1841-52.

[3] Huerta Fernández, S. Mechanics of masonry vaults: the equilibrium approach. In: Paulo Lourenço and Pere Roca (Eds.): Proc. of the 3rd International Seminar, Guimarães, Portugal (2001).

[4] Pugi, F. and Galassi, S. Seismic analysis of masonry voussoir arches according to the Italian building code. Ing. Sismica-Ital. (2013) 30,3:33-55.

[5] Galassi, S., Ruggieri, N. and Tempesta, G. A novel numerical tool for seismic vulnerability analysis of ruins in archaeological sites. Int. J. Archit. Herit. (2018) 14(1): 1-22, 10.1080/15583058.2018.1492647.

[6] Galassi, S. Ruggieri, N. and Tempesta, G. Ruins and archaeological artifacts: vulnerabilities analysis for their conservation through the original computer program BrickWORK. In: Aguilar, R., Torrealva, D., Moreira, S., Pando, M., Ramos, L.F. (Eds.), Proc. of 11th International Conference on structural analysis of historical constructions (SAHC2018), Cusco, Perù (2018), pp. 1839-1848.

[7] Cavalagli, N. Gusella, V. and Severini, L. Lateral loads carrying capacity and minimum thickness of circular and pointed masonry arches. Int. J. Mech. Sci. (2016) 115:645–56.

[8] Dimitri, R. and Tornabene, F. A parametric investigation of the seismic capacity for masonry arches and portals of different shapes. Eng. Fail. Anal. (2015) 52:1–34.

[9] Zampieri, P., Simoncello, N. and Pellegrino, C. Structural behavior of masonry arch with no horizontal springing settlement, Frattura ed Integrità Strutturale (2018) 43:182-190, 10.3221/IGF-ESIS.43.14.

[10] Zampieri, P., Simoncello, N. and Pellegrino, C. Seismic capacity of masonry arches with irregular abutments and arch thickness. Constr. Build. Mater. (2019) 201:786-806, 10.1016/j.conbuildmat.2018.12.063.

[11] Zampieri, P., Amoroso, M. and Pellegrino, C. The masonry buttressed arch on spreading support. Structures (2019) 20:226-236, 10.1016/j.istruc.2019.03.008.

[12] Zampieri, P., Cavalagli, N., Gusella, V. and Pellegrino, C. Collapse displacements of masonry arch with geometrical uncertainties on spreading supports. Comput. Struct. (2018) 208:118-129, 10.1016/j.compstruc.2018.07.001.

[13] Heyman, J. The safety of masonry arches. Int. J. Mech. Sci. (1969) 11,4:363-85, 10.1016/0020-7403(69)90070-8.

[14] Tempesta, G. and Galassi, S. Safety evaluation of masonry arches. A numerical procedure based on the thrust line closest to the geometrical axis. Int. J. Mech. Sci. (2019) 155:206-21, 10.1016/j.ijmecsci.2019.02.036.

[15] Galassi, S. and Tempesta, G. The Matlab code of the method based on the Full Range Factor for assessing the safety of masonry arches. MethodsX (2019) 6:1521-42, 10.1016/j.mex.2019.05.033.

[16] O’Dwyer, D. Funicular analysis of masonry vaults, Comput. Struct. (1999) 73:187-197, 10.1016/S0045-7949(98)00279-X.

[17] Block, P. and Ochsendorf, J. Thrust network analysis: a new methodology for threedimensional equilibrium, J. Int. Assoc. Shell. Spat. Struct. (2007) 48(3).

[18] Marmo, F. and Rosati, L. Reformulation and extension of the thrust network analysis, Comput. Struct. (2017) 182:104-118, 10.1016/j.compstruc.2016.11.016.

[19] Block, P. and Lachauer, L. Three-dimensional funicular analysis of masonry vaults, Mech. Res. Commun. (2014) 56:53-60, 10.1016/j.mechrescom.2013.11.010.

[20] Fraddosio, A., Lepore, N. and Piccioni, M.D. Thrust surface method: An innovative approach for the three-dimensional lower bound Limit Analysis of masonry vaults, Eng. Struct. (2020) 202:109846, 10.1016/j.engstruct.2019.109846.

### Document information

Published on 30/11/21
Submitted on 30/11/21

Volume Numerical modeling and structural analysis, 2021
DOI: 10.23967/sahc.2021.298
Licence: CC BY-NC-SA license

### Document Score

0

Views 38
Recommendations 0